A car is moving on a straight road due north with a uniform speed of 50km h^-1 when it turns left through 90°. It the speed remains unchanged after turning, the change in the velocity of the car in the turning process is :
Let the North be represented by Y axis. The when the car turns left, it moves along the -ve x axis, towards West.
Let
Change in velocity is = \vec{v2}-\vec{v1}=-50\hat{i}-50\hat{j}\ kmph
Magnitude of change in velocity=sqrt{50^2+50^2}=50\sqrt{2}
Direction of the change in velocity = South west , 45 deg. from South towards West.
To find the change in velocity of the car during the turning process, we need to consider the initial, or pre-turning, velocity and the final, or post-turning, velocity.
Let's break down the problem step by step:
Step 1: Determine the initial velocity.
The car is initially moving due north with a uniform speed of 50 km/h. Since it is moving due north, the initial velocity can be represented by a vector pointing straight up.
Initial velocity = 50 km/h (upward)
Step 2: Determine the final velocity.
After the car turns left through 90°, the direction of its velocity changes. Since the turning process doesn't affect the speed of the car, the magnitude of the final velocity will remain the same (50 km/h).
However, the final velocity will now be in the direction of the left turn, which is towards the west. We need to find the vector representation of the final velocity.
Final velocity = 50 km/h (west)
Step 3: Calculate the change in velocity.
To find the change in velocity, we need to subtract the initial velocity vector from the final velocity vector.
Change in velocity = Final velocity - Initial velocity
To perform this subtraction, we subtract the x-components separately and the y-components separately.
Final velocity (x-component) = -50 km/h (westward)
Initial velocity (x-component) = 0 km/h (there is no initial velocity in the x-direction)
Change in velocity (x-component) = -50 km/h (westward)
Final velocity (y-component) = 0 km/h (there is no final velocity in the y-direction)
Initial velocity (y-component) = 50 km/h (upward)
Change in velocity (y-component) = 0 km/h (no change)
Now we can write the change in velocity as a vector:
Change in velocity = -50 km/h (westward) + 0 km/h (upward)
Therefore, the change in velocity of the car during the turning process is:
Change in velocity = -50 km/h (westward)